Research Papers

Distributed Operational Space Formulation of Serial Manipulators

[+] Author and Article Information
Kishor D. Bhalerao

Software Engineer
Immersive Technologies,
Perth, WA 6017, Australia;
Honorary Research Fellow,
University of Melbourne,
Melbourne, VIC 3010, Australia
e-mail: kishorb@unimelb.edu.au

James Critchley

Lake Orion, MI 48362
e-mail: James@multibody.org

Denny Oetomo

Senior Lecturer
Department of Mechanical Engineering,
University of Melbourne,
Melbourne, VIC 3010, Australia
e-mail: doetomo@unimelb.edu.au

Roy Featherstone

Department of Advanced Robotics,
Istituto Italiano di Tecnologia,
Genova 16163, Italy
e-mail: roy.featherstone@ieee.org

Oussama Khatib

Department of Computer Science,
Stanford University,
Stanford, CA 94305
e-mail: ok@cs.stanford.edu

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 2, 2013; final manuscript received September 9, 2013; published online October 30, 2013. Assoc. Editor: Parviz Nikravesh.

J. Comput. Nonlinear Dynam 9(2), 021012 (Oct 30, 2013) (10 pages) Paper No: CND-13-1118; doi: 10.1115/1.4025577 History: Received June 02, 2013; Revised September 09, 2013

This paper presents a new parallel algorithm for the operational space dynamics of unconstrained serial manipulators, which outperforms contemporary sequential and parallel algorithms in the presence of two or more processors. The method employs a hybrid divide and conquer algorithm (DCA) multibody methodology which brings together the best features of the DCA and fast sequential techniques. The method achieves a logarithmic time complexity (O(log(n)) in the number of degrees of freedom (n) for computing the operational space inertia (Λe) of a serial manipulator in presence of O(n) processors. The paper also addresses the efficient sequential and parallel computation of the dynamically consistent generalized inverse (J¯e) of the task Jacobian, the associated null space projection matrix (Ne), and the joint actuator forces (τnull) which only affect the manipulator posture. The sequential algorithms for computing J¯e, Ne, and τnull are of O(n), O(n2), and O(n) computational complexity, respectively, while the corresponding parallel algorithms are of O(log(n)), O(n), and O(log(n)) time complexity in the presence of O(n) processors.

Copyright © 2014 by ASME
Topics: Algorithms
Your Session has timed out. Please sign back in to continue.


Khatib, O., 1987. “A Unified Approach for Motion and Force Control of Robot Manipulators: The Operational Space Formulation,” IEEE J. Robotics and Automation, 3(1), pp. 43–53. [CrossRef]
Khatib, O., Brock, O., Chang, K., Ruspini, D., Sentis, L., and Viji, S., 2003, “Robots for the Human and Interactive Simulations,” Proceedings of the 11th World Congress in Mechanism and Machine Science, Tianjin, China, pp. 1572 –1576.
Kreutz-Delgado, K., Jain, A., and Rodriguez, G., 1992, “Recursive Formulation of Operational Space Control,” Int. J. Robotics Res., 11(4), pp. 320–328. [CrossRef]
Lilly, K., and Orin, D., 1993, “Efficient o(n) Recursive Computation of the Operational Space Inertia Matrix,” IEEE Trans. Systems, Man and Cybernetics, 23(5), pp. 1384–1391. [CrossRef]
Chang, K., and Khatib, O., 2000, “Operational Space Dynamics: Efficient Algorithms for Modeling and Control of Branching Mechanisms,” Proceedings of the IEEE International Conference on Robotics and Automation, Vol. 1, pp. 850–856.
Wensing, P., Featherstone, R., and Orin, D., 2012, “A Reduced-Order Recursive Algorithm for the Computation of the Operational-Space Inertia Matrix,” Proceedings of ICRA 2012. IEEE International Conference on Robotics and Automation, pp. 4911–4917.
Featherstone, R., 2010, “Exploiting Sparsity in Operational-Space Dynamics,” Int. J. Robotics Res., 29(10), pp. 1353–1368. [CrossRef]
Fijany, A., 1994, “Schur Complement Factorizations and Parallel O(logn) Algorithms for Computation of Operational Space Mass Matrix and its Inverse,” Robotics and Automation, 1994, Proceedings of the 1994 IEEE International Conference on IEEE, pp. 2369–2376.
Jain, A., 2010, Robot and Multibody Dynamics: Analysis and Algorithms, Springer Verlag, Berlin.
Fijany, A., and Featherstone, R., 2013, “A New Factorization of the Mass Matrix for Optimal Serial and Parallel Calculation of Multibody Dynamics,” Multibody System Dynamics, 29(2), pp. 169–187. [CrossRef]
Bhalerao, K. D., Critchley, J., and Anderson, K., 2012, “An Efficient Parallel Dynamics Algorithm for Simulation of Large Articulated Robotic Systems,” Mech. Mach. Theory, 53, pp. 86–98. [CrossRef]
Nakanishi, J., Cory, R., Mistry, M., Peters, J., and Schaal, S., 2008, “Operational Space Control: A Theoretical and Empirical Comparison,” Int. J. Robotics Res., 27(6), pp. 737–757. [CrossRef]
Featherstone, R., 1999, “A Divide-and-Conquer Articulated Body Algorithm for Parallel O(log(n)) Calculation of Rigid Body Dynamics. Part 1: Basic Algorithm,” Int. J. Robotics Res., 18(9), pp. 867–875. [CrossRef]
Featherstone, R., 1999, “A Divide-and-Conquer Articulated Body Algorithm for Parallel O(log(n)) Calculation of Rigid Body Dynamics. Part 2: Trees, Loops, and Accuracy,” Int. J. Robotics Res., 18(9), pp. 876–892. [CrossRef]
Lathrop, R., 1985, “Parallelism in Manipulator Dynamics,” Int. J. Robotics Res., 4(2), pp. 80–102. [CrossRef]


Grahic Jump Location
Fig. 2

Notation for a serial manipulator

Grahic Jump Location
Fig. 3

Divide and conquer algorithm

Grahic Jump Location
Fig. 4

Time comparison for computing Je and Jex

Grahic Jump Location
Fig. 5

Time comparison for computing Λe-1 and βe

Grahic Jump Location
Fig. 6

Time comparison for computing Λe-1 and βe

Grahic Jump Location
Fig. 7

Load balancing for computing Λe-1 and βe for the 512 body chain

Grahic Jump Location
Fig. 8

Time comparison for computing Λe-1 and βe

Grahic Jump Location
Fig. 9

Time comparison for computing J¯e

Grahic Jump Location
Fig. 10

Time comparison for computing Ne



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In